Gain-Scheduled QSR-Dissipative Systems: An Input-Output Approach

Logan Anderson, Ryan James Caverly, Andrew G. Lamperski

Abstract: This paper presents a framework for the gain scheduling of QSR-dissipative systems and quantifies the resulting QSR-dissipative properties of the overall gain-scheduled system. This work constitutes a generalization of prior work in the literature involving the gain scheduling of passive and conic systems, providing a practical extension to non-square QSR-dissipative systems. The derived results are presented for two classes of systems that account for many well-known special cases of QSR-dissipative systems, including passive, conic, and finite L<inf>2</inf> gain systems. Special cases of the developed theory are shown to match closely to existing results in the literature. A numerical example is included that demonstrates the benefits of the derived results within the context of gain-scheduled control, with a comparison to passivity-based control.